RU2167518C2 - Method for determining information contents of bee family acoustic signal spectrum components when recognizing their state - Google Patents

Abstract

FIELD: medicine. SUBSTANCE: method involves both defining standardized intensity value in every narrow frequency bandwidth (25-30 Hz) and determining stability depending on intensity variations of different signal instances. Information capacity coefficients are determined for every pair of states to be diagnosed from every selected frequency bandwidth. Minimum set of bee family acoustic signal spectrum components is built. Total information capacity is calculated in every selected narrow frequency bandwidth based on all pairs of diagnosed states. Those pairs of states are selected which differentiation fails on the set of information signs tested. Total information capacity is calculated for these pairs of states over the remaining frequency bandwidths. Bandwidth is selected to be the next one if it has maximum total information capacity on the given pairs of classes. Selection process is continued in the same manner until adequate values of information capacity coefficient values are assigned to all pairs of classes in at least one selected narrow frequency bandwidth. EFFECT: accelerated analysis time. 3 cl, 7 tbl

Description

 The invention relates to the field of beekeeping and can find application in practical work on individual and collective apiaries.

There is a method of recognizing the state of the bee family by the acoustic noise emitted by it by spectral analysis and measuring the amplitudes of individual spectral components [1, 2]. Its disadvantages are:
the absence of clear quantitative criteria for recognizing specific states of bee colonies and a certain classification algorithm (only qualitative differences in amplitude spectra for various states are indicated);
a large number of informative signs by which the recognition of various states should be carried out (these signs are the average signal values in narrow frequency bands with a width of 25-30 Hz, and there are 20-25 such frequency bands and they cover the frequency range from 60 to 600 Hz).

 These shortcomings make it difficult to recognize specific conditions of bee colonies, increase the analysis time, do not provide the ability to quantify the reliability of recognition and complicate the hardware (or software) implementation of recognition tools.

 The technical problem to which the invention is directed is to reduce the number of informative features (analyzed narrow frequency bands) by using quantitative criteria for the information content of these signs and selecting the most informative ones, which will allow us to build an optimal classifier (decision rules) and also significantly simplify the hardware (or software) implementation of recognition tools and reduce analysis time.

где I_ij ^t - измеренная интенсивность сигнала в i-ой полосе частот при j-м состоянии пчелиной семьи для t-ой реализации сигнала.The solution to this problem is carried out in three stages. At the first stage, the informativeness coefficients of each informative sign are determined for recognition of specific conditions of the bee family. The initial data for solving this problem is a list of recognizable states (S _j , where j = 0, 1, 2,., N, and S ₀ is the normal state) and the amplitude or energy spectra of acoustic signals taken for them, which are represented by the average rectified signal values in narrow frequency bands (width 25-30 Hz), covering the range from 60 to 600 Hz. For each state, it is desirable to have at least m = 10 signal realizations (and, accordingly, their spectra) so that the stability of the spectral components can be estimated. Then the values of the spectral components averaged over these realizations will be called the intensities of the spectral components I _ij , where i = 1, 2, .., n are the serial numbers of the spectral bands, j = 0, 1, 2, .., N are the recognized states of the bee family

where I _ij ^t is the measured signal intensity in the i-th frequency band at the j-th state of the bee family for the t-th signal implementation.

Далее по ним определяются коэффициенты вариаций ν_ij как отношения среднеквадратических отклонений интенсивностей к их усредненным значениям

и уже по ним определяются стабильности
C_ij = 1-ν_ij. (4)
Чтобы устранить влияние коэффициента передачи приемного тракта (микрофона и усилителя) на измеренные значения спектральных составляющих сигнала, производится их нормирование относительно среднеквадратического значения всего сигнала в анализируемой полосе частот (60 - 600 Гц).To assess the stability C _{ij of} these intensities for each j-th state of the bee colony, the variance of D _ij intensities is determined by m signal realizations

Further, they are used to determine the coefficients of variation ν _ij as the ratio of the standard deviations of the intensities to their average values

and they are already determined by stability
C _ij = 1-ν _ij . (4)
In order to eliminate the influence of the transmission coefficient of the receiving path (microphone and amplifier) on the measured values of the spectral components of the signal, they are normalized with respect to the rms value of the entire signal in the analyzed frequency band (60 - 600 Hz).

 The easiest way to standardize is hardware, by introducing an AGC (automatic gain control) into the receiving path, the control signal for which is received from the output of the rms detector, to the input of which the amplifier receives an output signal with a passband from 60 to 600 Hz. In this case, the spectral components of the signal extracted using narrow-band filters or by calculation (using the discrete Fourier transform) will be normalized with respect to the rms value of the signal for the entire analyzed frequency band (60 - 600 Hz).

 If the numerical method of spectral analysis is used, it is preferable to use not the amplitude, but the energy spectra of the signal, since they are more stable and can be determined by shorter implementations of the signal.

Thus, the initial data are represented by two matrices, dimension n • (N + 1), one of which consists of intensities I _ij , and the second of their stability C _ij .

Using these two matrices, one can calculate the informativity coefficients J _jk ^{i of} each i-th spectral band to recognize each of the pairs j and k states:
J $\genfrac{}{}{0ex}{}{\text{i}}{\text{j}}$ _k = | I _ij -I _ik | • C _ij • C _ik = | ΔI $\genfrac{}{}{0ex}{}{\text{i}}{\text{j}}$ _k | • C _ij • C _ik , (5)
where j, k = 0, 1, 2, ..., N, and j ≠ k.

где R - число сочетаний из (N+1) по два.For each i-th spectral band of such pairs of states there will be

where R is the number of combinations of (N + 1) in two.

Это позволяет ранжировать спектральные полосы по их информативности для распознавания данных состояний.Thus, informativeness coefficients J _jk ⁱ constitute a matrix of dimension n • R. We determine the total informativeness of each spectral band for all pairs of states

This allows us to rank the spectral bands according to their information content for recognition of these states.

 However, the total informativeness coefficients characterize the average informativeness of a given narrow frequency band over all pairs of states. In this case, some pairs of states can be separated very well (the difference between the signal intensities in a given frequency band is large), while others can be poorly separated (the difference between the signal intensities for the corresponding states is small and lies within their variations for different signal implementations for the same states) . Therefore, for such poorly distinguishable pairs of states, it is necessary to look for other narrow frequency bands for which precisely these pairs of states differ well, i.e. have rather large values of informativity coefficients (although the total informativity coefficient for all pairs of classes can be significantly lower). Obviously, the more informative features will be used for recognition (narrow frequency bands), the, in principle, the more reliable the recognition of a given set of states can be made, but the more difficult will be the decision rules used for recognition, and therefore the recognition device that implements them . Therefore, the problem arises of selecting the minimum required number of informative features (narrow frequency bands) for reliable recognition of a given set of states. It is this problem that is being solved at the second stage.

It is proposed to solve it as follows. At the first step, a narrow frequency band is selected that provides the maximum total information content for all pairs of classes -J $\genfrac{}{}{0ex}{}{\text{i}}{\text{Σ}}$ _max (in accordance with criterion (7)). Then, some critical value of the coefficient of information _content J _{jk (kp) is assigned} , which distinguishes between good or bad separation of any pair of states.

где R- число всех пар состояний.As a guideline for choosing J _{jk (kp),} you can use

where R is the number of all pairs of states.

All informativity coefficients for the narrow frequency band selected at the first step are compared with this critical value and all rows of the informativity coefficient matrix for which J _jk ⁽¹⁾ ≥ J _{jk (kp) are crossed} out. The column corresponding to the first selected narrow frequency band J _jk ^{(1) is also} _deleted (here, the superscript in parentheses indicates the step number).

At the second step, the total informativity coefficients for all remaining narrow frequency bands are again calculated from the matrix remaining after deleting the rows and column, and the frequency band corresponding to the maximum value of total informativeness is selected. The pair informativeness coefficients of this frequency band J _jk ^{(2) are} also compared with J _{jk (kp)} and rows for which J _jk ⁽²⁾ exceed J _{jk (kp) are} deleted from the matrix. If even after this step not all pairs of states differ quite well, then the selection process continues further, i.e. a third informative feature is selected, etc.

где J $\genfrac{}{}{0ex}{}{\text{(}}{\text{Σ}}$ ^q) - суммарный коэффициент информативности выбранного на данном q-ом шаге столбца; p - общее число вычеркнутых на предыдущих шагах строк.If at some qth step all the paired informativity coefficients J _jk ^{(q) of the} selected column are less than the initially assigned critical value, then it should be reduced. You can use the same criterion.

where j $\genfrac{}{}{0ex}{}{\text{(}}{\text{Σ}}$ ^q) is the total coefficient of information content of the column selected at this qth step; p is the total number of lines deleted in the previous steps.

 The process of selecting informative features (the number of steps) should continue until each of the pairs of recognized states in at least one of the selected informative features has a sufficiently large value of the coefficient of information content (more than the critical value).

 And, finally, the third stage consists in constructing decisive rules (classifier), which, based on the informative features selected at the previous stage, reliably recognize any of the given possible states of the bee family.

 It is proposed to determine the decision rules in the form of algebraic equations defining the boundaries of regions in a multidimensional space of selected informative features corresponding to each recognizable state (taking into account possible variations of individual implementations of the same states).

Let d <n informative features be selected as a result of the second stage (as our experience shows, the value of d lies in the range from 2 to 5, depending on a given number N of recognized states). The values of the informative features are the normalized values of the noise signal intensities averaged over m realizations in the selected narrow frequency bands I _ij (see expression (1)).

Центры областей d - мерного пространства, соответствующих заданным (N+1) состояниям будут определяться уравнениями

Здесь: у₀, y₁,..., y_i,... y_N - выходные величины решающего устройства, соответствующие каждому из заданного множества состояний; а_ij - постоянные коэффициенты уравнений, которые и требуется определить.As a result, for all (N + 1) given states we will have a matrix

The centers of the regions of the d - dimensional space corresponding to the given (N + 1) states will be determined by the equations

Here: y ₀ , y ₁ , ..., y _i , ... y _N are the output values of the resolver corresponding to each of a given set of states; and _ij are the constant coefficients of the equations that are required to be determined.

In fact, each of these equations transforms the d-dimensional space of informative features into the one-dimensional space of the productive feature of _i . Now, in order to fully determine the decision rules, it is necessary, firstly, to determine the unknown coefficients a _ij , and secondly, to specify the upper and lower boundaries of each resultant attribute y _i corresponding to the boundaries of recognized states.

h_i - нормирующий множитель;
J_ik ⁱ - коэффициенты информативности.The constant coefficients a _ij should determine the specific contribution of each informative attribute (and these are the measured values of I _i ) in the corresponding resultant attribute. It is logical to accept this contribution proportional to the sum of the distinguishing abilities of this attribute (the ability to distinguish a given state from all other given states). And they are determined by the corresponding informativity coefficients J _ik ⁱ . Therefore, it is advisable to determine the weights a _ij in the form
a _ij = J $\genfrac{}{}{0ex}{}{\text{i}}{\text{j}}$ _k • h _j • b _ij , (12)
Where

h _i is the normalizing factor;
J _ik ⁱ - informativeness factors.

 This is equivalent to the generally accepted method for determining unknown coefficients in regression equations in metric problems (where the object is characterized not by different qualitative states, but by different values of the output quantitative attribute). Indeed, in such problems, the coefficients of the linear regression equation (weighting coefficients of the equation linking the productive output quantity with informative features) are found from the condition of their proportionality by the partial derivatives of the output quantity with respect to the corresponding informative attribute.

Naturally, depending on the sign of the increment of the informative feature ΔI _jk during the transition of the object from the jth state to the kth, and the weighting factors a _ij can have different signs. Therefore, in the expression (13), the signs of the informativity coefficients should be taken into account, whereas before that we were only interested in their absolute value, which was determined in accordance with (5). To account for the sign, it is necessary to determine J _ik ⁱ as
J _jk ⁱ = (I _ij -I _ik ) • C _ij • C _ik (14)
It differs from (5) only in that the difference (I _ij -I _ik ) is taken taking into account its sign.

In this case, it is obvious that b _ij found by (13), and therefore a _ij found by (12), can have different signs.

If there are no restrictions on the admissible values of the effective features (which occurs with the digital method of implementing the recognition device), then the normalizing factor h _i can be taken equal to unity.

If, however, restrictions are imposed on the maximum permissible values of the effective attribute (which occurs with the analogue method of implementing the recognition device), then the normalizing factor h _{i is} selected so that y _jmax corresponds to (0.7 - 0.9) y _jdop . The limitation of the normalizing factor from below is due to the fact that in analog devices, at low signal levels, errors increase.

Now it remains only to determine the boundaries of each state according to the corresponding effective signs of _jgr . The most correct solution to this problem under conditions when the initially specified set of states (N + 1) is far from exhausting the entire set of possible states of the bee family is to limit each state to bilateral boundaries with centers defined in accordance with Eqs. (11) and the width of the intervals, depending from the variance of the signal intensities in the narrow frequency bands used for these states for various signal implementations.

попадает примерно 95% всех реализаций, можно рекомендовать именно таким образом определять границы состояний

где D_ij - дисперсии интенсивностей в i-м узком диапазоне частот при j-м состоянии, определяемая по m реализациям сигнала в соответствии с (2).Given that under the normal law of distribution of the values of informative features in the interval width

about 95% of all implementations fall in, we can recommend that in this way determine the boundaries of states

where D _ij are the dispersions of intensities in the ith narrow frequency range under the jth state, determined by m realizations of the signal in accordance with (2).

и, откладывая их по обе стороны от центров состояний y_j, определять границы каждого состояния. При нахождении интервалов Δy_j в соответствии с (16) используются модули коэффициентов a_ij, т.к. в (15) в каждой скобке стоят знаки (±), а это значит, что при любом знаке соответствующего коэффициента результаты будут получаться одни и те же.Obviously, the boundaries of individual states determined in this way will be located symmetrically with respect to their centers defined by equations (11). Therefore, it is more convenient to determine the intervals Δy _j between the center of each j-th state and its boundaries, which can be found from the equations

and laying them back on both sides of the state centers y _j , determine the boundaries of each state. When finding the intervals Δy _j in accordance with (16), the moduli of the coefficients a _{ij are used} , since in (15) in each bracket there are signs (±), which means that for any sign of the corresponding coefficient, the results will be the same.

Thus, the decision rules are fully constructed. They can be implemented in two types of recognition devices: digital and analog (regardless of how narrow frequency bands are extracted from the noise signal and the signal intensities are measured in them, which can also be implemented in various ways). The digital implementation method assumes the presence of a processor that digitally receives the measured normalized values of the signal intensities l _ij in the selected d narrow frequency bands, substitutes them into equations (11), calculates the values of the effective attribute y ₀ , y ₁ , y ₂ , ... , y _N and compares them with pre-calculated boundaries for each of the recognized states. In this case, in principle, three outcomes are possible:
1. If only for one of the equations of system (11) the calculated value of _{j j} falls into the allowed interval between the upper and lower boundary values, then this implementation of the signal corresponds to this particular jth state. 2. If for any of the equations the value of y _j does not fall between the boundaries of a given state, this will indicate that this implementation of the signal corresponds to a state not included in the given set N. Such a situation is quite likely, since the real states of the bee family depend from many factors that can overlap each other, which can lead to an almost unlimited set of possible conditions, from which we initially select only some of the beekeeper who are most interested in the state.

а, например,

Такую перестройку распознающей системы легко осуществить при любом способе ее реализации.3. And, finally, in principle, a third outcome is possible, when more than one state is simultaneously recognized. This will indicate that the boundaries of the regions corresponding to given states in the d-dimensional space intersect, which can happen if the separability of these pairs of states determined by the corresponding pair informativity coefficients is insufficient. In this case, it is necessary to increase the dimensionality of the space of informative features, i.e. add another narrow frequency band, which requires a complete overhaul of the entire recognition system. To avoid this, one can try to narrow the boundaries of the corresponding intersecting states, i.e., in the corresponding equations from the system of equations (15), the acceptable boundaries of the intensity variations are not accepted

but for example

Such a restructuring of the recognition system is easy to implement with any method of its implementation.

With the analog implementation method, the recognition device consists of (N + 1) analog adders with d-inputs each, and the transmission coefficients for each of the inputs correspond to the values of the weight coefficients a _ij . Two comparators are connected to the output of each adder, tuned respectively to the upper and lower boundaries of the corresponding effective attribute y _j , and the outputs of each pair of comparators are connected to a logic circuit that is triggered when the output signal of the adder is in the interval between the thresholds of operation of the respective comparators. The outputs of the logic circuits are connected to signal LEDs that light up when one of the given states is recognized.

Example:
We illustrate all the above with a concrete example.

Let us set the following set of recognizable states of the bee family:
S ₀ is normal;
S ₁ - loss of the uterus;
S ₂ - the adoption of a new uterus;
S ₃ - rejection of the new uterus;
S ₄ - pre-break condition;
S ₅ - overheating of the hive.

 For each of these states, m = 12 realizations of acoustic signals were recorded and their amplitude spectra were obtained, which are represented by normalized signal intensities in narrow frequency bands with a width of 30 Hz, uniformly distributed in the range from 60 to 570 Hz (total n = 17 frequency bands, i.e., i = 1,2, ..., 17). The normalization of the spectral components was carried out in hardware, using the AGC built into the preamplifier.

Они образуют матрицу размерностью n(N+1), т.е. 17•6 представленную табл. 1.According to these normalized values determined for each t-th implementation of the signal, in accordance with (1), the intensities of the spectral components averaged over all realizations were found for the j-th state

They form a matrix of dimension n (N + 1), i.e. 17 • 6 presented table. 1.

А затем по (3) определялись коэффициенты вариации

и по (4) стабильности этих спектральных составляющих:
C_ij= l-ν_ij
Имея усредненные по всем m реализациям сигналов значения интенсивностей l_ij и стабильностей C_ij спектральных составляющих для каждой i-ой полосы частот и каждого j-ого состояния, по формуле (5) вычисляем коэффициенты информативности каждой из этих спектральных полос для различения любой j-ой пары состояний - J_jk.Further, in accordance with (2), the variance of each spectral component was determined for all m realizations:

And then, from (3), the coefficients of variation were determined

and according to (4) the stability of these spectral components:
C _ij = l-ν _ij
Having the values of intensities l _ij and stability C _{ij of} spectral components averaged over all m signal implementations for each i-th frequency band and each j-th state, by formula (5) we calculate the informativeness coefficients of each of these spectral bands to distinguish any j-th pairs of states - J _jk .

 As a result, we obtain a matrix of informativity coefficients of dimension n • R, i.e. in our case, 17 • 15. This matrix is presented in table. 2.

After summing the informativeness coefficients for each narrow frequency band (according to criterion (3)), we obtain the total informativeness coefficients of these spectral components by distinguishing all pairs of states. They are represented by the first of the additional rows of the table. 2 as the sum of its columns J∑ ¹ .

Затем из табл.2 вычеркиваем те строки, в которых выбранный информативный признак дает значения коэффициента информативности J_jk > J_jk(кp) = 17,6. В нашем случае будут вычеркнуты строки 2 (J₀₂ = 23,4), 3 (J₀₃ = 33,8), 4 (J₀₄ = 23,7), 6 (J₁₂= 23,4), 10 (J₂₃ = 33,7), 11 (J₂₄ = 32,3) и 12 (J₂₅ = 36,7).At the first step, we select a feature that has the maximum value of criterion (7). In our case, the frequency band 210-240 Hz corresponds to it. We calculate (8) the critical value of the coefficient of information content

Then, from table 2, we delete those rows in which the selected informative attribute gives the values of the coefficient of informativeness J _jk > J _{jk (cr)} = 17.6. In our case, lines 2 (J ₀₂ = 23.4), 3 (J ₀₃ = 33.8), 4 (J ₀₄ = 23.7), 6 (J ₁₂ = 23.4), 10 (J ₂₃ = 33.7), 11 (J ₂₄ = 32.3) and 12 (J ₂₅ = 36.7).

For the remaining lines, for all signs, except for the one already selected, the total informativeness coefficients are again calculated and the next sign that has the maximum value of this coefficient is selected. For our case, this will be the spectral component corresponding to the band 420-450 Hz (J∑ ² = 181). Thus, in the second step, we must choose an informative feature corresponding to the frequency band 420-450 Hz.

Further, using the same rule, we delete from the truncated table the column corresponding to this frequency band and the rows where the values of the information coefficient in this column are J _jk > J _{jk (kp)} There are three such rows: third J ₁₃ = 29.9, sixth J ₃₄ = 45.2 and the seventh J ₃₅ = 72.7. For the remaining rows and columns, we again calculate the total coefficient of information content. It is maximum at the column corresponding to the frequency band 300-330 Hz (J∑ ³ = 128.5). Therefore, in the third step, we must choose this particular frequency band.

Next, cross out this column and the rows where J _jk in this column is greater than J _{jk (kp)} . These will be the lines corresponding to J ₀₅ (26.6), J ₁₄ (37.5), J ₁₅ (47.3).

For the remaining lines, and there are only two left: J ₀₁ and J ₄₅ , we again calculate the values of the criterion J∑ ⁴ and analyze the signs with the maximum values of the criterion J∑ ⁴ . They correspond to frequency bands of 240-270 Hz (J _4Σ = 56.4), 180-210 Hz (J _4Σ = 50.2), 390-420 Hz (J _4Σ = 45.9). According to the values of this criterion, these frequency bands differ only slightly. However, since in this case it determines the total separability of two pairs of states, it is advantageous to take the one that provides good separability of both pairs of states as the fourth and last informative feature. A frequency band of 390-420 Hz corresponds to this condition. Although in terms of total information content it is inferior to the first two, but each of the remaining two pairs of states differs quite well for them (J ₀₁ = 17.8 and J ₄₅ = 28.1), while the informative feature corresponding to the maximum of J∑ ⁴ , distinguishing well states 4 and 5 (J ₄₅ = 53.1), poorly distinguishes between zero and first states (J ₀₁ = 3.3).

 So, for the recognition of these six states was enough four informative signs corresponding to the frequency bands 210-240 Hz, 420-450 Hz, 300-330 Hz and 390-420 Hz.

при переходе пчелиной семьи от одного состояния к другому могут быть различных знаков, то и весовые коэффициенты могут иметь различные знаки, в то время как в табл. 2 знаки приращений информативных признаков не учитывались.Now it remains only to determine the optimal values of the weighting coefficients in equations (11) that relate the values of the output quantities that recognize the system Y _j with informative features I _i . Since increments of informative features

when the bee family moves from one state to another, there can be different signs, then the weighting factors can have different signs, while in the table. 2 signs of increments of informative signs were not taken into account.

Therefore, for the selected four narrow frequency bands, we present the values of the informativeness coefficients taking into account their sign. These data, as well as the corresponding values of the averaged normalized signal values l _ij and their standard deviations, determined by m = 12 spectral realizations, are presented in Table. 3. All these data are necessary to determine the weight coefficients a _ij and the boundaries of the diagnosed states.

Найденные значения b_ij представлены в табл. 4. Эти значения могут непосредственно использоваться в качестве весовых коэффициентов а_ij в цифровых распознающих системах (поскольку для них можно значения всех нормирующих множителей h_j принять равным единице).First, we will find the values of the coefficients b _ij . In accordance with expression (13), they are equal to the algebraic sums of the informativity coefficients for all diagnosed states

The found values of b _{ij are} presented in table. 4. These values can be directly used as weighting factors a _ij in digital recognition systems (since for them the values of all normalizing factors h _{j can} be taken equal to one).

 For analog recognition systems this cannot be done, because the voltage at the outputs of the adders should not exceed the maximum permissible values. In addition, in analog recognition systems it is advisable, if possible, to simplify the structure, i.e. on adders that select certain states, not all 4 signals (from narrow-band channels) should be started, but only the most informative of them (just to isolate this state), which is easy to determine from the corresponding informativeness factors.

 In particular, it is advisable to add signals from the 1st and 3rd frequency channels to the adder that selects the zero state, and not start from the 2nd and 4th. Indeed, states 0-2 are well separated along the first channel; 0-3 and 0-4 (the corresponding values of the informativeness coefficients are 23.4; 33.8 and 23.7). To separate the pairs of states 0-1 and 0-5, it is enough to use the 3rd channel (the corresponding informativity coefficients are 16.4 and 26.6).

To select the first state, in general, only one 3rd channel is sufficient, since on this channel, all informativity coefficients are quite large (J ₁₀ = 16.4, J ₁₂ = 24.9, J ₁₃ = 21.5, J ₁₄ = 37.5, J ₁₅ = 47.3).

To select the second state, it is also sufficient to start the signal from only one 1st channel (J ₂₀ = 23.4, J ₂₁ = 23.4, J ₂₃ = 33.7, J ₂₄ = 32.3, J ₂₅ = 36.7 )

To isolate the third state, a signal from one 2nd channel is also sufficient (J ₃₀ = 22.2, J ₃₁ = 29.9, J ₃₂ = 21.7, J ₃₄ = 45.2, J ₃₅ = 72.7).

 To select the 4th and 5th states, signals from all 4 frequency channels are needed.

Given these simplifications of the recognition device, the values of the coefficients b _ij will change. For a simplified structure, these values are given in table. 5.

Now we can begin to determine the necessary values of the normalizing factors h _j . To obtain a numerical solution, we set the voltage values at the outputs of narrow-band channels equal to the normalized average values of the corresponding intensities, multiplied by 0.1 V. As a result, we obtain the following matrix of signals at the outputs of narrow-band channels for all diagnosed conditions of the bee family (in volts).

Для нахождения масштабных коэффициентов h_j используем условие, чтобы при любом из диагностируемых состояний максимальный выходной сигнал любого сумматора не превышал 0,8 U_доп (0,8 U_доп взято с учетом возможности превышения отдельных реализаций сигнала над усредненными значениями, приведенными в матрице (17)).

To find the scale factors h _{j, we} use the condition that, for any of the diagnosed states, the maximum output signal of any adder does not exceed 0.8 U _extra (0.8 U _extra taken taking into account the possibility of exceeding individual implementations of the signal over the average values given in the matrix (17 )).

In general, this condition can be written
U $\genfrac{}{}{0ex}{}{\text{(k}}{\text{Σj}}$ ⁾ = h _j (b _1j I _1k + b _2j I _2k + ... + b _dj + I _dk ) ≈ 0.8 U _add , (18)
Here u $\genfrac{}{}{0ex}{}{\text{(k}}{\text{Σj}}$ ⁾ is the voltage at the output of the adder emitting je state of the bee family for the case when in reality it is in the kth state, with k = 0, 1, 2, ..., N.

Obviously, h _j must be obtained for a k such that U $\genfrac{}{}{0ex}{}{\text{(k}}{\text{Σj}}$ ⁾ as much as possible.

затем взять из них максимальное значение и из него найти h_j. Приняв U_доп = 10 B, все результаты вычислений сведем в табл. 6.For this, it is necessary to calculate for all values of k the expressions written in parentheses

then take the maximum value from them and find h _j from it. Taking U _add = 10 B, we summarize all the calculation results in table. 6.

Аналогично определяем остальные нормирующие множители:

Теперь можно определить весовые коэффициенты а_ij = b_ijh_j Их значения представлены матрицей (19):

(19)
Коэффициенты a_ij представляют собой коэффициенты передачи сумматоров по каждой из суммирующих цепей.From this table it can be seen that at the output of the first adder, the maximum voltage will be at state S ₁ . From here

Similarly, we determine the remaining normalizing factors:

Now we can determine the weighting coefficients a _ij = b _ij h _j Their values are represented by the matrix (19):

(19)
The coefficients a _ij are the transfer coefficients of the adders for each of the summing chains.

 When applying to the inputs of the adders voltage represented by the matrix (17), the outputs of the adders will be formed voltage, presented in table. 7.

приведены в абсолютном виде, а при переходе от усредненных интенсивностей сигнала I_ij к значениям сигналов, действующих на входах сумматоров мы вводим коэффициент 0,1 (В). Этот же коэффициент необходимо учитывать и в выражении (16). В итоге получаем
Δy₀ = 0,512 • 2 • 0,96 + 0,554 • 2 • 0,68 = 1,74;
Δy₁ = 0,85 • 2 • 0,6 = 1,02
Δy₂ = 0,842 • 2 • 0,35 = 0,59;
Δy₃ = 0,843 • 2 • 0,66 = 1,11;
Δy₄ = 0,693 • 2 • 0,39 + 0,149 • 2 • 0,44 + 0,589 • 2 • 0,37 + 0,57 • 2 • 0,51 = 1,69;
Δy₅ = 0,18 • 2 • 0,87 + 0,434 • 2 • 0,08 + 0,361 • 2 • 0,25 + 0,375 • 2 • 0,14 = 0,67.Now it remains only to calculate the boundary intervals of states and determine their boundaries. To do this, we use the expression (16), but we must take into account that the data given in Table 3 standard deviations

are given in absolute form, and in the transition from the average signal intensities I _ij to the values of the signals acting at the inputs of the adders, we introduce a coefficient of 0.1 (V). The same coefficient must be taken into account in expression (16). As a result, we get
Δy ₀ = 0.512 • 2 • 0.96 + 0.554 • 2 • 0.68 = 1.74;
Δy ₁ = 0.85 • 2 • 0.6 = 1.02
Δy ₂ = 0.842 • 2 • 0.35 = 0.59;
Δy ₃ = 0.843 • 2 • 0.66 = 1.11;
Δy ₄ = 0.693 • 2 • 0.39 + 0.149 • 2 • 0.44 + 0.589 • 2 • 0.37 + 0.57 • 2 • 0.51 = 1.69;
Δy ₅ = 0.18 • 2 • 0.87 + 0.434 • 2 • 0.08 + 0.361 • 2 • 0.25 + 0.375 • 2 • 0.14 = 0.67.

Thus, the boundaries of the state S ₀ on the output voltage of the adder Σ ₀ will be from y _0n = 6.01-1.74 = 4.27 V to Y _0v = 6.01 + 1.74 = 7.75 V.

The closest value to these boundaries from below is the signal at state S ₅ equal to 4.03 V, and above - at state S ₂ equal to 7.85 V. As you can see, there is still some margin to the boundaries of state S ₀ , i.e. by the output signal of the adder Σ ₀ these classes do not overlap. Thus, the comparators connected to the output of this adder must be tuned to threshold voltages U _0n ≈ 4.3 V, U _0v ≈ 7.7 B
Similarly, we obtain the threshold voltage of the comparators connected to the outputs of the remaining adders:
U _1n = 8.00 - 1.02 ≈ 7 B, U _1c = 8.00 + 1.02 ≈ 9B;
U _2n = 8.00 - 0.59 ≈ 7.4 V, U _2c = 8.00 + 0.59 ≈ 8.6 B;
U _3n = 8.00 - 1.11 ≈ 6.9 B, U _3c = 8.00 + 1.11 ≈ 9.1 B;
U _4n = 8.00 - 1.69 ≈ 0.4 V, U _4c = 8.00 + 1.69 ≈ 3.8 B;
U _5n = 8.00 - 0.67 ≈ 2.3 V, U _5c = 8.00 + 0.67 ≈ 3.7 B;
Note: The output voltages of the adders Σ _{4 /} and Σ _{5 /} in accordance with table. 7 for all conditions of the bee colony are negative. Therefore, they can be inverted and the minus sign not taken into account, which is what was done in the calculation of threshold voltages.

 A comparison of the obtained boundary stresses with the nominal output voltages for other conditions of the bee family (from the diagnosed set of conditions) shows that all other states do not intersect with the boundaries of the states being distinguished. Thus, the recognition of diagnosed conditions will be very reliable (with a confidence probability of no worse than 0.95).

Sources of information
1. Yeskov E.K. Acoustic signaling of public insects. - M .: Science. 1979.

 2. Eskov E.K. Management of vital processes of honey bees and their optimization. - M .: All-Union Academy of Agricultural Sciences named after V.I. Lenin. - 1982.

 3. J. Tu. R. Gonzalez. Pattern recognition principles. - M .: Mir, 1978, p. 177. (Trained classifiers of images, deterministic approach).

 4. Fundamentals of metrology and electrical measurements. Ed. EAT. Dushina. - L .: Energoatomizdat, 1987.

 5. Shindovsky E., Schurts O. Statistical methods of quality management / Control norms and control plans / Per. from German. - M .: Mir, 1976-579 p.

Claims (3)

 1. A method for determining the informativeness of the spectral components of the acoustic signal of bee colonies when recognizing their states, which consists in obtaining the amplitude or energy spectrum of the acoustic noise produced by the bee colony in a previously limited frequency range from 60 to 600 Hz and extracting normalized values of the intensity of the spectral components averaged over several signal implementations in the selected narrow frequency bands, jointly covering the entire specified frequency range, I distinguish Keep in mind that for each narrow frequency band, in addition to the normalized intensity value, stability is determined, depending on the variation of the intensity values for different signal implementations, by preliminary determining the intensity dispersions for these realizations in this narrow frequency band, and then informativeness coefficients for each pair of recognized states are determined for each allocated frequency band.  2. The method according to p. 1, characterized in that to determine the optimal set of spectral components from their informativeness coefficients, the total informativeness of each selected narrow frequency band is determined for all pairs of diagnosed states and the frequency band with the maximum total informational content is selected first, then state pairs with informativeness factors having low values for a given narrow frequency band, and for these pairs of states, the total informativeness for all remaining the frequency bands and the next one select the band that has the maximum total information content for these pairs of classes, and then the selection continues in such a way until all pairs of classes are characterized by sufficient values of the information coefficients for at least one of the selected narrow frequency bands.  3. The method according to claim 2, characterized in that they select the optimal weighting coefficients of linear algebraic equations that determine the boundaries of the states of the bee family, which are used in the construction of decision rules for reliable recognition of states, while the selection of weighting coefficients uses the values of signal intensities in the corresponding narrow frequency bands and determine them in the form of total values of the informativity coefficients for all distinguished pairs of states multiplied by the normalizing factor spruce, determined from the conditions for obtaining output signals in the desired range.

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